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<div class="section" id="exercises">
<h1><a class="toc-backref" href="./tutorial-metafunctions.html#id60" name="exercises">Exercises</a></h1>
<dl>
<dt>1-0.</dt>
<dd>Use <tt class="literal"><span class="pre">BOOST_STATIC_ASSERT</span></tt> to add error checking to the <tt class="literal"><span class="pre">binary</span></tt>
template presented in section <a class="reference" href="./resources.html">1</a>.4.1 so
that <tt class="literal"><span class="pre">binary&lt;N&gt;::value</span></tt> causes a compilation error if <tt class="literal"><span class="pre">N</span></tt>
contains digits other than <tt class="literal"><span class="pre">0</span></tt> or <tt class="literal"><span class="pre">1</span></tt>.</dd>
<dt>1-1.</dt>
<dd>Turn <tt class="literal"><span class="pre">vector_c&lt;int,1,2,3&gt;</span></tt> into a type sequence with elements
(2,3,4) using <tt class="literal"><span class="pre">transform</span></tt>.</dd>
<dt>1-2.</dt>
<dd>Turn <tt class="literal"><span class="pre">vector_c&lt;int,1,2,3&gt;</span></tt> into a type sequence with elements
(1,4,9) using <tt class="literal"><span class="pre">transform</span></tt>.</dd>
<dt>1-3.</dt>
<dd>Turn <tt class="literal"><span class="pre">T</span></tt> into <tt class="literal"><span class="pre">T****</span></tt> by using <tt class="literal"><span class="pre">twice</span></tt> twice.</dd>
<dt>1-4.</dt>
<dd>Turn <tt class="literal"><span class="pre">T</span></tt> into <tt class="literal"><span class="pre">T****</span></tt> using <tt class="literal"><span class="pre">twice</span></tt> on itself.</dd>
<dt>1-5.</dt>
<dd><p class="first">There's still a problem with the dimensional analysis code in
section 1.1.
Hint:  What happens when you do:</p>
<pre class="literal-block">
f = f + m * a;
</pre>
<p>Repair this example using techniques shown in this
chapter.</p>
<!-- @ example.wrap('''void will_fail%s
{ quantity<float,force> f(m*a);
''' % ma_function_args, '}')
stack[:0] = dimensional_analysis # stick support code in
compile('all', expect_error = True) -->
</dd>
<dt>1-6.</dt>
<dd>Build a lambda expression that has functionality equivalent to
<tt class="literal"><span class="pre">twice</span></tt>.  Hint: <tt class="literal"><span class="pre">mpl::apply</span></tt> is a metafunction!</dd>
<dt>1-7*.</dt>
<dd><p class="first">What do you think would be the semantics of the following 
constructs:</p>
<pre class="literal-block">
typedef mpl::lambda&lt;mpl::lambda&lt;_1&gt; &gt;::type t1;
typedef mpl::apply&lt;_1,mpl::plus&lt;_1,_2&gt; &gt;::type t2;
typedef mpl::apply&lt;_1,std::vector&lt;int&gt; &gt;::type t3;
typedef mpl::apply&lt;_1,std::vector&lt;_1&gt; &gt;::type t4;
typedef mpl::apply&lt;mpl::lambda&lt;_1&gt;,std::vector&lt;int&gt; &gt;::type t5;
typedef mpl::apply&lt;mpl::lambda&lt;_1&gt;,std::vector&lt;_1&gt; &gt;::type t6;
typedef mpl::apply&lt;mpl::lambda&lt;_1&gt;,mpl::plus&lt;_1,_2&gt; &gt;::type t7;
typedef mpl::apply&lt;_1,mpl::lambda&lt; mpl::plus&lt;_1,_2&gt; &gt; &gt;::type t8;
</pre>
<!-- @example.prepend('#include <vector>')
compile() -->
<p class="last">Show the steps used to
arrive at your answers and write tests verifying your assumptions. 
Did the library behavior match your reasoning? If not, analyze the 
failed tests to discover the actual expression semantics.
Explain why your assumptions were different, what
behavior you find more coherent, and why.</p>
</dd>
<dt>1-8*.</dt>
<dd>Our dimensional analysis framework dealt with dimensions, but it
entirely ignored the issue of <em>units</em>.  A length can be
represented in inches, feet, or meters.  A force can be
represented in newtons or in kg m/sec<sup>2</sup>.  Add the
ability to specify units and test your code.  Try to make your
interface as syntactically friendly as possible for the user.</dd>
</dl>
<!-- Along with Alan Turing, Church was one of the founders of computer
science. -->
<!-- yes, this is easier to read, but the real beauty of ``apply`` is that
it not only works on metafunction classes, but on metafunctions passed
with placeholder arguments.   -->
<!-- Naturally, MPL defines a series of these numbered placeholder
types, so that we can handle metafunctions with more arguments. -->
<!-- : in order to pass a template in  the ``BinaryOperation`` position,
``transform`` would have to be declared::

 template <
     class Sequence1, class Sequence2
   , template <class,class> class BinaryOperation
 >
 struct transform;  // returning a sequence -->
<!-- "Programming with types" -->
<!-- Once again, a nested ``value`` member is optional for
metafunctions, and required for integral type wrappers. -->
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